Abstract
This article provides a critical commentary on the concepts of representation and digital artefacts in Morgan and Kynigos’s article of this Special Issue. To set the context, in the first part, I examine some of the tensions that arose during discussions through the 1980s and 1990s about representation in mathematics education research. Then, I comment on the conceptual differences between Morgan’s and Kynigos’s approaches. These differences point to different epistemological assumptions that lead to different conceptualizations of artefacts in learning processes. In the last part, I argue that Morgan’s and Kynigos’s approaches have the merit of moving the discussion about representations to new theoretical horizons. I suggest, however, that a discussion about representations and digital artefacts requires a thematized account of the manner in which the phenomenological artefact- and representation-mediated knowledge produced by students in the classroom relates to the target cultural mathematical knowledge. Such an account, I contend, requires an explicit ontological conception of knowing and knowledge. I conclude the article with an example in which knowledge is considered as codified movement and knowing as the event of its enactment in concrete practice. Within this Hegelian materialist viewpoint, representations are neither predicated in terms of an adequacy between ideas and their representations nor as heuristic devices in meaning making processes. Representations are rather an integral part of the activity of knowledge presentation.
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Notes
For a more detailed discussion of Leibniz’ representational view of knowledge, see Radford (2013a).
Constructionism is a neo-Kantian theory of learning based on Piaget’s epistemology. As Resnick describes it,
Constructionism is based on two types of ‘construction.’ First, it asserts that learning is an active process, in which people actively construct knowledge from their experiences in the world. People don’t get ideas; they make them. (This idea is based on the constructivist theories of Jean Piaget.) To this, constructionism adds the idea that people construct new knowledge with particular effectiveness when they are engaged in constructing personally-meaningful products. (Resnick, 1996, p. 2; emphasis in the original)
“Es la mañana llena de tempestad/ en el corazón del verano. // Como pañuelos blancos de adiós viajan las nubes, / el viento las sacude con sus viajeras manos.” (Neruda, 1976, p. 8)
For instance, they play with the stones; see http://www.youtube.com/watch?v=bpRu1Zg-128
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This article is a result of a research program funded by the Social Sciences and Humanities Research Council of Canada (SSHRC/CRSH).
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Radford, L. On the role of representations and artefacts in knowing and learning. Educ Stud Math 85, 405–422 (2014). https://doi.org/10.1007/s10649-013-9527-x
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DOI: https://doi.org/10.1007/s10649-013-9527-x